This paper describes the syntheses of core/shell gold nanoparticles stabilized with a monolayer of double hydrophilic block copolymer and their stimuli responsiveness before and after shell cross-linking. The hybrid nanoparticles consist of gold core, cross-linkable poly(2-(dimethylamino)ethyl methacrylate) (PDMA) inner shell, and poly(ethylene oxide) (PEO) corona. First, diblock copolymer PEO-b-PDMA was prepared via the reversible addition-fragmentation chain transfer (RAFT) technique using a PEO-based macroRAFT agent. The dithioester end group of PEO-b-PDMA diblock copolymer was reduced to a thiol end group. The obtained PEO-b-PDMA-SH was then used to prepare diblock copolymer stabilized gold nanoparticles by the "grafting-to" approach. 1,2-Bis(2-iodoethoxy)ethane (BIEE) was utilized to selectively cross-link the PDMA residues in the inner shell. The stimuli responsiveness and colloidal stability of core/shell gold nanoparticles before and after shell cross-linking were characterized by laser light scattering (LLS), UV-vis transmittance, and transmission electron microscopy (TEM). At pH 9, the average hydrodynamic radius Rh of non-cross-linked hybrid gold nanoparticles starts to increase above 35 degrees C due to the lower critical solution temperature (LCST) phase behavior of the PDMA blocks in the inner shell. In contrast, Rh of the shell cross-linked gold nanoparticles were essentially independent of temperature. Core/shell gold nanoparticles before and after shell cross-linking exhibit reversible swelling on varying the solution pH. Compared to non-cross-linked core/shell gold nanoparticles, shell cross-linking of the hybrid gold nanoparticles leads to permanent core/shell nanostructures with much higher colloidal stability and physically isolates the gold core from the external environment.